SOLUTION: Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5. Find the probability that x = 3 using the binomial tables. Use the normal approximat

Question 230588: Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5. Find the probability that x = 3 using the binomial tables. Use the normal approximation to find the probability that x = 3. Show all work.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5. Find the probability that x = 3 using the binomial tables.
P(x=3) = 15C3(0.5)^3*(0.5)^12 = 0.0139..
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Use the normal approximation to find the probability that x = 3. Show all work.
Note: mean = np = 15*0.5 = 7.5 ; std = sqrt(npq) = sqrt(7.5*0.5) = 1.9365..
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P(x=3) = P(2.5 < x < 3.5)
z(2.5) = (2.5-7.5)/1.9365 = -2.5820
z(3.5) = (3.5-7.5)/1.9365 = -2.0656
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P(2.5 < x < 3.5) = P(-2.5820 < z < -2.0656) = 0.0145
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Cheers,
Stan H.
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